Capability with Small Samples
Six Sigma – iSixSigma › Forums › Old Forums › General › Capability with Small Samples
 This topic has 5 replies, 2 voices, and was last updated 13 years, 9 months ago by Anonymous.

AuthorPosts

January 3, 2009 at 11:01 pm #51599
I have a question about conducting a capability study on a small number of parts. I manufacture cylinders that go through a broaching process to cut several grooves into the I.D. The cylinders are very expensive and I currently only have 5 parts.
We measure the depth of the groove at 5 different lengths along the cylinder ( 75mm, 150mm, etc) and at 0, 120, 240 degrees around the cylinder. So each cylinder has 15 depth measurements.
Im trying to look at the capability of this process, but Im not sure I can use the data I have. Can I use the 75 data points for each cylinder to calculate the capability? I dont have logical subgroups like a textbook capability study i.e. 20 subgroups of 35 measurements.
Ive looked through numerous references and cant seem to find anything similar to this. Im happy to research more if someone can point me in the right direction.
Go Vikings.
Thanks
0January 4, 2009 at 3:49 am #179245Have you already addressed the accuracy and precision of your measurement system and determined stability and distribution type?
0January 4, 2009 at 4:46 am #179246Once you validate the measurement system, I believe your next step is to determine the stability of your process prior to the capability study. This requires that you preserved the time order of your data collection. If you have then you should be able to develop a subgrouping strategy that makes sense (ie minimizes the within subgroup” variation) using 75 observations.
I am not aware of any hard and fast rules for determining subgroup size or frequency, although with continuous data and your limited data set, I would think n=3 and k=25 would be appropriate with an XbarR Chart.
If stable, you can conduct your capability study based on distribution type and specification characteristics.
75 continuous measures are sufficient to hang your statistical hat on I believe, and if reporting shortterm capability, I believe it should work as your initial baseline measure.
But doublecheck this info. Best of luck.0January 4, 2009 at 9:10 am #179247You should use a Shewhart chart to try and find sources of variation. This means in practice plotting charts in a variety of ways. Years ago when we had no software this was tedious so we used Multivari charts to find sources of variation.My advice therefore is to first use what you have and try to find all the sources of variation.You should also be aware that Minitab used Anova which assumes independence. If your data is not independent – which you can check using a scatter diagram, then you can use a graphical method to estimate the contribution of each souce.Typically, you will have machine to machine, and along the tube ( tag the ends if you can.)Remember, if you want to check temporal stability you would need to form subgroups where each sample within a subgroup is collected in the order of manufacture. Don’t use random samples taken out of a Bin.Cheers,
Andy0January 4, 2009 at 10:44 pm #179258Thanks Andy/newbie,
We did have issues with the measurement device initially, but we resolved those problems and moved forward with the study.
I have already looked at the data on a multivari and within piece variation is greatest.
My heartburn is in creating subgroups after the data has already been collected. I have a list of 75 data points. I don’t have data that was collected as 25 subgroups of n=3. The best I might be able to use is the subgroups of the angular measurements, so I have 15 subgroups of n=5. Something doesn’t feel right, but it might just be my lack of confidence.
Thanks again.
Matt0January 5, 2009 at 9:43 am #179260Hi Matt,If you know the largest source of variation, you’re in an excellent position to do something about it. (This is a common feature with semiconductor furnaces.)Have you tagged your components so you know which way up they went through your machining processes? Sometimes it is possible to reverse orientation in one of the process steps so that the form cancels out the opposing form in a later step.If you can’t do this then you might have to try and understand some machining effects.For example, in a process for grinding image setter drums, there can be differences between the front and the back ID of the drum – two hemicylindrical drums pinned together to form a cylindrical drum.If your in a similar situation you might want to check your jig and fixings for flexing under resistance.As for capability, I can’t comment any further as I don’t understand your circumstances. But I personally always try to distinguish the process mean from the process uniformity. By uniformity, I mean the variation within piece. In fact, I ofte prefer to plot the process mean and the process uniformity on separate Shewhart Xbar and R charts.A common mistake and one that set Motorola back many years was to regard sample measurements taken within a piece as a subgroup for temporal variation. Don’t make the same mistake.If you take three measurements within a piece, the average of the three measurements is only one member of the set of n in a Shewhart Chart. In other words, you would need 9 measurements for n = 3 because n is made up of three averages of within piece.I hope this is clear …Good luck,
Andy0 
AuthorPosts
The forum ‘General’ is closed to new topics and replies.